Only aggregates intermix, no reaction occurs

Mixing on molecular level, reaction occurs

Only aggregates intermix, no reaction occurs

FIGURE 5.1 Macrofluid and microfluid Idealizations (from Levenspiel, 1972).

Two extremes of molecular mixing are traditionally known as microfluid and macrofluid. In microfluid, species are completely mixed on a molecular scale, while in macrofluid, there is no mixing on a molecular scale although the lumps of fluid are macroscopically well mixed. When miscible reactants are brought together to react in a reactor, the extent of mixing may control the reactor performance. Consider the case of a reactor carrying out reactions between two reactants A and B as shown in Fig. 5.1. Reactants A and B are introduced into the reactor in separate streams. Two extremes of microfluid and macrofluid may be considered. When reactants A and B are mixed on a molecular scale at a rate much faster than the reaction rate (microfluid), reaction will occur and the effective rate will be controlled by reaction kinetics. When reactants A and B are mixed macroscopically but are not mixed on a molecular scale (macrofluid), virtually no reaction can take place. Real systems will behave in an intermediate way, exhibiting A-rich and B-rich regions with partial segregation. In many fast reactions (compared to mixing) and high viscosity systems (such as polymerization reactions), the mixing process interacts with chemical reactions and may significantly influence the reactor performance (product distribution, product quality and so on). The traditional methods of finding the upper and lower limits on performance by employing the microfluid and macrofluid concepts are useful to guide the base-line design. Detailed fluid dynamics based modeling and simulations of interaction between mixing and chemical reactions may, however, lead to enhanced understanding and the capability to tailor the reactor performance. This chapter is restricted to the analysis of turbulent reactive mixing. Before discussing modeling approaches, it is useful to consider a physical picture of turbulent mixing and to estimate the relevant length and time scales to determine whether the reaction is 'fast' or 'slow'.

The basic concepts and physical picture of turbulence were discussed in Chapter 3. As discussed there, fluid motions of several scales co-exist in turbulent flows. Vortex stretching continuously forms small-scale fluid motions from large-scale motions. Kinetic energy is transferred to progressively smaller scales during this process. At the smallest scale, energy is irreversibly dissipated into heat at a rate e, the turbulent energy dissipation rate. These smallest scales are called Kolmogorov scales and are defined as

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